Structure instability and nonlinear evolution of magnetic islands produced by time-dependent magnetic reconnection at the magnetopause are studied. The analytic expression for the width of magnetic islands and critical conditions for the occurrence of bifurcation and chaos are derived. It is shown that the magnetic islands are unstable against the interference from external disturbances. Their structure can be destroyed by medium and small-scale solar wind turbulences, leading to stochastic magnetic reconnection and the formation of irregular small-scale structures in magnetospheric boundary regions.¿ 1997 American Geophysical Union